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Sine and Cosine
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Sine and Cosine: Derivative

[d/dx](sin(x)) = cos(x)

Alternate notation
sin'(u) = cos(u)u'
D(sin(u)) = cos(u)D(u)
dsin(u) = cos(x)du
[d/dx](cos(x)) = -sin(x)
Alternate notation
cos'(u) = -sin(u)u'
D(cos(u)) = -sin(u)D(u)
dcos(u) = -sin(x)du
See the derivation of this.